3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

  • 3

    Pair Of Linear Equations In Two Variables

    This section covers the representation and solution of pairs of linear equations in two variables using graphical and algebraic methods.

  • 3.1

    Introduction

    This section introduces the concept of pair of linear equations in two variables through relatable examples and outlines the methods to represent and solve these equations.

  • 3.2

    Graphical Method Of Solution Of A Pair Of Linear Equations

    This section introduces the graphical method for solving pairs of linear equations in two variables, detailing conditions for consistent, inconsistent, and dependent equations.

  • 3.3

    Algebraic Methods Of Solving A Pair Of Linear Equations

    This section explores algebraic methods for solving pairs of linear equations, focusing on substitution and elimination methods.

  • 3.3.1

    Substitution Method

    The Substitution Method is an effective algebraic technique used to solve pairs of linear equations by expressing one variable in terms of the other and substituting it into the other equation.

  • 3.3.2

    Elimination Method

    The elimination method is a systematic approach to solving pairs of linear equations by removing one variable to simplify the equations.

  • 3.4

    Summary

    This section provides a concise overview of various methods to solve a pair of linear equations in two variables, including graphical and algebraic approaches.

    • Key Summary

    Exploration of pair of linear equations in two variables offers insights into graphical and algebraic methods for finding solutions. Key concepts include identifying consistent, inconsistent, and dependent systems of equations while analyzing their graphical representations. Various mathematical representations and methods to approach these equations are emphasized throughout the chapter.

    Key Takeaways

    • Understanding the representation of pairs of linear equations in two variables.
    • Applying graphical and algebraic methods to solve linear equations.
    • Identifying the nature of solutions based on the intersection of lines.

    Key Concepts

    • Consistent Pair of Linear Equations: A pair of linear equations that has at least one solution. Graphically, represented by two intersecting lines.
    • Inconsistent Pair of Linear Equations: A pair of linear equations that do not have any solutions, represented by parallel lines.
    • Dependent Pair of Linear Equations: A pair of linear equations that has infinitely many solutions, represented by coincident lines.
    • Graphical Method: A method of solving linear equations by plotting their graphs and identifying points of intersection.
    • Algebraic Methods: Techniques like substitution and elimination used to solve pairs of linear equations by manipulating the equations algebraically.